At least 1 day before you plan to serve the dessert, combine the flours, salt, and 2 tablespoons of the sugar in a mixer fitted with a dough hook, and mix. Dissolve the yeast in the water. With the mixer running at low speed, add the yeast mixture to the flour mixture. Add the eggs and mix well. Add the butter and mix at medium speed until smooth, about 10 minutes. Do not skimp on the mixing time; this is how the dough gets kneaded. Place the dough in a deep container, cover tightly with plastic wrap, and then refrigerate overnight. The next day, turn the dough out onto a floured work surface. Flour your rolling pin and roll the dough into a 12-inch circle, about 1/2-inch thick. Transfer to an ungreased cookie sheet. Loosely drape plastic wrap over the dough and let rise in a warm place until doubled in bulk, 1 to 2 hours.
Meanwhile, make the custard by combining the milk and vanilla bean in a small saucepan and bring just to a boil over medium heat. Immediately turn off the heat and set aside to infuse for 10 minutes. Whisk the egg yolks and granulated sugar together until light and fluffy. Add the cornstarch and whisk vigorously until no lumps remain. Whisk in 1/4 cup of the hot milk mixture until incorporated. Whisk in the remaining hot milk mixture, reserving the empty saucepan.
Pour the mixture through a strainer back into the saucepan. Cook over medium-high heat, whisking constantly, until thickened and slowly boiling. Remove from the heat and stir in the butter. Pour into a bowl and cover with plastic wrap, lightly pressing the plastic against the surface to prevent a skin from forming. Chill at least 2 hours or until ready to use. (The custard can be made up to 2 days in advance and kept refrigerated.)
Preheat the oven to 350 degrees F. Remove the plastic wrap from the dough and sprinkle with the remaining 2 tablespoons sugar. Bake until golden brown, 15 to 20 minutes. After 10 minutes, rotate the pan to ensure even cooking. When baked, immediately remove to a wire rack and let cool to room temperature.
Not more than 2 hours before serving, use a serrated knife to slice the round of brioche horizontally in half. Spread the bottom generously with the custard. Place the top brioche on and press lightly. Using a heavy, large serrated knife, cut into wedges, and serve topped with powdered sugar. Serve within 2 hours.